Question

A small company manufactures a certain product. The price-production relationship for this product is P = -0.7*D + 300, where P is the unit sales price of the product and D is the annual production (number of units produced). Suppose variable costs are $25 per unit produced and fixed costs are $10,287 . Find the break even point (minimum number of units that must be produced for a business to become profitable). Note: there are 2 roots in the breakeven equation, choose the smallest root.

Answer 1

Answer:42 units

Step-by-step explanation:

Given

Price-production relationship=-0.7D+300

Total cost=Fixed cost+ variable cost

Total cost=10,287+25D

where D is the units produced

Total revenue
`=\left ( -0.7D+300\right )D`

Total revenue
`=-0.7D^2+300D`

For Break even point

Total revenue=Total cost

`10,287+25D=-0.7D^2+300D`

`7D^2-2750D+102870=0`

`D=(2750\pm √(2750^2-4* 7* 102870))/(2* 7)`

`D=41.869\approx 42` units